The cable structure in the figure is loaded at mid$-$span by a concentrated force. The cable is linear elastic with axial stiffness of $EA=2{10}^5$ units. The structure is obviously unstable in the undeformed configuration. It is$,$ therefore, essential to consider equilibrium in the deformed configuration. We will study two cases: $($a$)$ no prestress, and $($b$)$ a prestressing force of $2000$ units. Because of symmetry in geometry and loading, the structure has a single free global DOF, which is the vertical translation under the force. Determine the forcedisplacement relation under the exact nonlinear equilibrium and the Green$-$Lagrange strain. Plot this relation for the two prestressing force values and comment on the resulting behavior. Determine the tangent stiffness matrix by differentiation of the resisting force and use it with the Newton$-$Raphson iteration to determine the vertical displacement under a concentrated force of $70$ units for the case of a prestressing force of $200$ units.